Die-hard fans support their team win or lose. Die-hard fans cheer just as loud after a great play when their team is 2-9 as they would if they were 9-2. However, sometimes a loss is in your team's long term best interest, so wouldn't rooting for your team to lose still be supporting them? I know I've already ticked off many readers and caused them to start yelling at their computer screen like I can hear them, but stay with me, I think you'll agree with my point if you're willing to look at this with reason and not emotion.
The word/term 'fan' is short for fanatic, so the natural tendency of a fan is to be deeply emotionally involved in the results of their favorite team week to week. Chest bumps and high fives when their team pulls off an upset or comeback victory, or cursing and breaking their remote control when they temporarily lose their mind after a crushing defeat are par for the course for die-hard fans. Merriam-Webster defines a fanatic as, "marked by excessive enthusiasm and often intense uncritical devotion," so to fans with that mindset, it's hard to introduce the idea of a loss being a good thing without it sounding like a foreign language. Those fans will label you as fair-weather when you mention this theory, but they're looking at the issue with short sighted vision.
Reasons To Root For Your Team To Lose:
The Draft - This only applies to the NFL in my opinion. The worst team in the NBA have only won the first overall pick four times since 1985 (last time in 2004) while using their current lottery system, so rooting for losses is pointless. Hell, the 3rd worst (seven times) and 5th worst team (five times) has won the first overall pick more times than the worst team in the NBA. I also wouldn't advocate rooting for failure in major league baseball since even the best players take two to three years to reach the big show and a lot of the top picks are high school kids which are a much riskier gamble.
In the NFL however, there are some examples of when rooting for your team to lose and gain the first overall pick is clearly the best move for their long term success. I'm not saying that the top overall pick in the NFL draft is a guarantee, far from it, but every several years there is prospect so talented that he's worth tanking the season (Andrew Luck, Eli Manning, Peyton Manning, Orlando Pace). If your team has 5-11 talent, wouldn't you rather them tank for the first pick rather than live up to expectations? Every loss hurts, but what do you gain from a 5-11 or 6-10 season? Are you going to buy a shirt to celebrate and remember the season? If you're going to be forced to suffer through a losing season, you might as well get something out of that misery by having the top overall pick. If your front office is competent, then that top pick should be an impact player capable of turning around the franchise very quickly. Is winning two or three more games in a season where you'll miss the playoffs either way really worth missing out on a franchise player?
Coaching Change - Your team has Norv Turner, Derek Dooley, Lane Kiffin, Dennis Franchione, or some other uninspiring coach that isn't capable of taking your team to the highest level. The worst result for a team each year is to be average and that's exactly what you'll be most years what that lifeless coach taking up space on the sidelines. No fan gets excited over an average season, and average seasons don't convince most owners or athletic directors that a change is necessary.
The reality is you're going to be stuck with that mediocre head coach for at least five years unless he hits rock bottom. If that coach's track record is that of an underachiever, why wouldn't you root for his quick departure? Think of it as rooting against that coach you know can't get the job done and not rooting against your team. You simply want what is best for your favorite team, and getting rid of that coach would be beneficial to their long term success. Isn't one painful season full of losses worth many more years of success? Would you rather deal with one 2-10 season or five 7-5 seasons before your team finally moves on and finds a better coach? I would rather deal with the one horrible season. Does that make me a bad fan? As a Texas Longhorn fan, of course I loved seeing my team crush Oklahoma earlier this year, but there's no doubt that another loss to their biggest rival would have moved Mack Brown off the hot seat and into the unemployment line. Moving on from Mack is in the best interest of my team, but that win over Oklahoma might have saved his job. I enjoyed that win, but if I had to choose between losing that game or keeping Mack; I'd take another loss.
My hope is always for my team to succeed. However, if failure in the short term is guaranteed, then why not root for the season to hit rock bottom to force a franchise altering move like hiring a new coach or gaining the top overall pick. If a fan is someone who cheers blindly without considering alternative strategies, then I'm not a fan; I'll start calling myself a supporter.